Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
27864.3-a1
27864.3-a
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
27864.3
\( 2^{3} \cdot 3^{4} \cdot 43 \)
\( 2^{10} \cdot 3^{16} \cdot 43^{3} \)
$3.26546$
$(a), (-a-1), (a-1), (-3a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$1$
$0.665946086$
0.941789987
\( \frac{21226369178}{19320201} a - \frac{50204656630}{19320201} \)
\( \bigl[a\) , \( a\) , \( a\) , \( -82 a - 21\) , \( 357 a - 286\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-82a-21\right){x}+357a-286$
27864.3-b1
27864.3-b
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
27864.3
\( 2^{3} \cdot 3^{4} \cdot 43 \)
\( 2^{10} \cdot 3^{6} \cdot 43^{7} \)
$3.26546$
$(a), (-a-1), (a-1), (-3a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \cdot 3 \)
$1$
$0.475602017$
2.017808469
\( \frac{4221782747113658}{7339102499889} a + \frac{29753937148295630}{7339102499889} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 68 a - 238\) , \( 512 a - 1058\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(68a-238\right){x}+512a-1058$
27864.3-c1
27864.3-c
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
27864.3
\( 2^{3} \cdot 3^{4} \cdot 43 \)
\( 2^{10} \cdot 3^{12} \cdot 43 \)
$3.26546$
$(a), (-a-1), (a-1), (-3a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \cdot 3^{2} \)
$0.118626377$
$1.873745711$
5.658214722
\( -\frac{187524338}{846369} a + \frac{1460733730}{846369} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3 a + 13\) , \( 2 a + 6\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+13\right){x}+2a+6$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.